In order to discuss direct-object and indirect-object pronouns, it will help us to first discuss direct objects and indirect objects in simple sentences:
Io do il libro a Gianni. = I give the book to Gianni.
In the example above, “the book” is the direct object and “Gianni” is the indirect object.
Direct objects are the people/places/things that most immediately receive the action of the verb. They are connected with the verb without prepositions, i.e., directly:
Mangiamo l’insalata prima. > La mangiamo prima. = We are eating it first.
Indirect objects are the people/places/things that are secondary receivers of the action of the verb. They are connected with their verbs (usually) through a preposition, i.e., indirectly.
Rispondo alla Professora Salvato domani. > Le rispondo domani. = I will respond to her tomorrow.
Positioning of pronouns
Pronouns will usually precede a conjugated verb in Italian. (This is the opposite of what we do in English), e.g.,
Ti vedo.
I see you.
Renato lo chiama.
Renato is calling him.
Non la compro perché non ho soldi.
I’m not buying it because I don’t have money. (The “it” in question is feminine singular.)
Quanto vedi Roberta? > La vedrò domani.
When are you seeing Roberta? > I will see her tomorrow.
However if you have a helper verb (modal auxiliary) like volere, dovere, potere or a verb that similary sets up an infinitive (pensare di, sperare di, preferire, sognare di, ecc,) then you will have the option of putting the pronoun in front of the conjugated helper verb, or at the end of the infinitive—after eliminating the final –e of the infinitive:
Non lo posso mangiare. OR Non posso mangiarlo.
I can’t eat it.
Ti volevo dire qualcosa importante. OR Volevo dirti qualcosa importante.
I wanted to tell you something important.
Ho comprato un quadro e vorrei mostrartelo. OR Ho comprato un quadro e te lo vorrei mostrare.
I bought you a picture and I want to show it to you.
Ho comprato il regalo a Maria e stasera penso di darglielo. OR Ho comprato il regalo a Maria e glielo voglio dare!
I bought the gift for Maria and I plan on giving it to her tonight.
Pronouns will also attach to command forms, except for formal commands, and some negative commands (see Section 3.1 on imperatives):
Dammelo. = Give it to me.
Dillo. = Say it!